In covered 3-quart saucepan, cook bacon, onion, thyme, and nutmeg over medium heat until onion is soft, about 10 minutes. Stir in broth and potatoes. Increase heat to high, and bring mixture to a boil. Reduce heat to low, and simmer until potatoes are tender, about 15 minutes.
Stir in corn, increase heat to high, and bring back to a boil. Stir in fish; cover and reduce heat to low. Cook chowder 5 minutes. Remove from heat, and stir in cream and parsley.